Sign Conventions and Systems of Thermodynamic Quantities

Sign Convention:

In thermodynamics, the standard sign convention is that energy added to a system in the form of heat is treated as positive, and energy added to a system in the form of work is taken as negative — HIP to WIN (heat in positive – work in negative). Although some literature states that all forms of energy added to a system, such as heat or work, are positive, this is a standard sign convention. While it is true that the sign convention established for heat and work interactions is important, it is also true that the indicated convention is abandoned later in the same text and replaced with magnitudes or absolute values. This is particularly true in the context of cycle analysis, in which the absolute value is utilised to calculate energy transfers across cycles. The fact that the ratio of energy added/rejected by heat transfer equals the ratio of the absolute temperatures of the thermal reservoirs is not proven for reversible cycles in general. This study develops the suitable relationship between energy transfers and thermal reservoir temperatures for reversible cycles, and then applies the results to both power producing and power consuming engineering equipment in order to encourage uniformity in sign conventions in the future.

The following are the sign conventions that we employ: Q indicates that there is net heat transfer into the system; W indicates that there is net work done by the system. If Q is positive, then there is net heat transfer into the system. As a result, positive Q contributes energy to the system, whereas positive W depletes energy from the system As a result, U = Q = W. When energy enters the system, the sign of the energy is positive. When energy exits the system, the sign of the energy is negative. If work is being done on the system, the system’s indication will be positive. If the system performs the job, the system’s sign is negative. As a result, the energy that enters the elephant’s front legs has a good connotation. The work done by the elephant on the performer is shown by a negative sign.

It must be remembered that one of the heat quantities is negative, out of a system, as it should be since the ratio of absolute temperatures is always positive. With reference to Arnas et al., (2003), we can examine the various details of this result particularly with respect to engine efficiency and refrigerator and heat pump coefficient of performances. For this demonstration, we will use the sign convention of Callen (1960) that all energy transfers into a system are positive and all out of the system are negative.

In thermodynamics, various sign conventions are used for energy transfers in the form of heat and work. Regardless of the sign convention introduced, thermodynamics texts subsequently abandon their established conventions in favour of magnitudes or absolute values. This article illustrates the importance of consistent use of a sign convention throughout a text and applies it to power-producing and power-consuming engineering devices. Additionally, using a selected sign convention, a substantive proof is presented showing why the ratio of energy added/rejected in the form of heat equals the ratio of the absolute temperatures of the energy source/sink, respectively.

CONCLUSION:

The sign convention commonly used by the thermodynamics community is that energy introduced to a system in the form of heat should be considered positive, while energy added in the form of work should be considered negative. This is denoted by the abbreviation HIP to WIN (heat is positive, work is negative).

The following is the General Rule for Allocating Signs in the following situations: When energy enters the system, the energy’s sign is positive, indicating that it is entering. In the event that energy is expelled from a system, the energy’s sign is negative. A positive system signal will be displayed if and when work is being done on a system.